Chapter 15, Problem 35E

1.

To determine

Determine the fixed selling and administrative cost allocated to each unit of LM Corporation’s mover.

Explanation of Solution

Cost-plus-markup approach: The pricing approach used by the companies to set the target selling price based on the cost plus desired profit, is referred to as cost-plus-markup approach.

Step 1: Calculate total unit cost.

$\begin{array}{c}\text{Selling price = Total unit cost + }\left(\text{Markup percent}\times \text{Total unit cost}\right)\\ \$450=\text{Total unit cost +}\left(12.5\%\times \text{Total unit cost}\right)\\ \$450=\text{Total unit cost}\times \left(12.5\%+100\%\right)\end{array}$

$\begin{array}{c}\text{Total unit cost}=\frac{\$450}{\left(12.5\%+100\%\right)}\\ =\frac{\$450}{1.125}\\ =\$400\end{array}$

Step 2: Calculate the allocated fixed selling and administrative cost.

Particulars	Cost per unit
Total unit cost	$400
Less: Variable manufacturing cost	$250
Less: Applied fixed manufacturing cost	$50
Less: Variable selling and administrative cost	$60
Allocated fixed and administrative cost	$40

Table (1)

Therefore, the fixed selling and administrative cost allocated to each unit of LM Corporation’s mover is $40.

2.

To determine

Develop a cost-plus pricing formula which should result in a target price of $450 per mover for:

1. (a) Variable manufacturing cost,
2. (b) Absorption manufacturing cost, and
3. (c) Total variable cost.

Explanation of Solution

(a) Cost-plus pricing formula for variable manufacturing cost.

Step 1: Calculate markup percentage.

$\begin{array}{c}\text{Markup percentage = }\frac{\left(\text{Target price}-\text{Variable manufacturing cost}\right)}{\text{Variable manufacturing cost}}\times 100\\ =\frac{\left(\$450-\$250\right)}{\$250}\times 100\\ =0.80\times 100\\ =80\%\end{array}$

Step 2: Develop a cost-plus pricing formula for variable manufacturing cost.

$\begin{array}{c}\text{Selling price = Variable manufacturing cost + }\left(\begin{array}{l}\text{Markup percent}\times \\ \text{Variable manufacturing cost}\end{array}\right)\\ \$450=\text{\$250 +}\left(80\%\times \$250\right)\end{array}$

(b) Cost-plus pricing formula for absorption manufacturing cost.

Step 1: Calculate absorption manufacturing cost.

Particulars	Cost per unit
Variable manufacturing cost	$250
Applied fixed manufacturing cost	$50
Absorption manufacturing cost	$300

Table (2)

Step 2: Calculate markup percentage.

$\begin{array}{c}\text{Markup percentage = }\frac{\left(\text{Target price}-\text{Absorption manufacturing cost}\right)}{\text{Absorption}\text{manufacturing cost}}\times 100\\ =\frac{\left(\$450-\$300\right)}{\$300}\times 100\\ =0.50\times 100\\ =50\%\end{array}$

Step 3: Develop a cost-plus pricing formula for absorption manufacturing cost.

$\begin{array}{c}\text{Selling price = Absorptionmanufacturing cost + }\left(\begin{array}{l}\text{Markup percent}\times \\ \text{Absorption manufacturing cost}\end{array}\right)\\ \$450=\text{\$300 +}\left(50\%\times \$300\right)\end{array}$

(c) Cost-plus pricing formula for total variable cost.

Step 1: Calculate total variable cost.

Particulars	Cost per unit
Variable manufacturing cost	$250
Variable selling and administrative cost	$60
$\text{Total variable cost}$	$310

Table (3)

Step 2: Calculate markup percentage.

$\begin{array}{c}\text{Markup percentage = }\frac{\left(\text{Target price}-\text{Total variable cost}\right)}{\text{Total variable cost}}\times 100\\ =\frac{\left(\$450-\$310\right)}{\$310}\times 100\\ =0.4516\times 100\\ =45.16\%\end{array}$

Step 3: Develop a cost-plus pricing formula for total variable cost.

$\begin{array}{c}\text{Selling price = Total varibale cost + }\left(\begin{array}{l}\text{Markup percent}\times \\ \text{Total varibale cost }\end{array}\right)\\ \$450=\text{\$310 +}\left(45.16\%\times \$310\right)\end{array}$